Anti-friction nut and screw mechanisms of a variety of designs have been proposed heretofore in efforts to increase the operating efficiency and to avoid certain shortcomings of prior designs. Constructions of this type are illustrated for example in U.S. Pat. Nos. 3,296,880; 3,648,535; 3,720,115; and 3,802,290. Although these constructions do reduce friction losses and contribute to the operating efficiency of nut and screw mechanisms, all are subject to serious defects and short life owing to various causes including serious wear occuring between the roller elements and the screw. A variety of proposals have been made to obviate these shortcomings but without success. Some of these proposals employ cylindrical roller elements in contact with the sidewall of a square thread, whereas others employ roller elements having contoured ends bearing against the side walls of Acme or modified Acme screw threads. In each of these designs the roller axis is shown and/or described as lying on a radius of the screw or the nut. Despite the foregoing and other expedients, none of these prior proposals for anti-friction screw and nut mechanisms have satisfactory service life and operating characteristics except possibly under low load operating conditions.